The emerging global infectious COVID-19 disease by novel Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) presents critical threats to global public health and the economy since it was identified in late December 2019 in China. The virus has gone through various pathways of evolution. To understand the evolution and transmission of SARS-CoV-2, genotyping of virus isolates is of great importance. This study presents an accurate method for effectively genotyping SARS-CoV-2 viruses using complete genomes. The method employs the multiple sequence alignments of the genome isolates with the SARS-CoV-2 reference genome. The single-nucleotide polymorphism (SNP) genotypes are then measured by Jaccard distances to track the relationship of virus isolates. The genotyping analysis of SARS-CoV-2 isolates from the globe reveals that specific multiple mutations are the predominated mutation type during the current epidemic. The proposed method serves an effective tool for monitoring and tracking the epidemic of pathogenic viruses in their global and local genetic variations. The genotyping analysis shows that the genes encoding the S proteins and RNA polymerase, RNA primase, and nucleoprotein, undergo frequent mutations. These mutations are critical for vaccine development in disease control.